Many decisions people make can be described as decisions under risk. Understanding the mechanisms that drive these decisions is an important goal in decision neuroscience. Two competing classes of risky decision making models have been proposed to describe human behavior, namely utility-based models and risk-return models. Here we used a novel investment decision task that uses streams of (past) returns as stimuli to investigate how consistent the two classes of models are with the neurobiological processes underlying investment decisions (where outcomes usually follow continuous distributions). By showing (a) that risk-return models can explain choices behaviorally and (b) that the components of risk-return models (value, risk, and risk attitude) are represented in the brain during choices, we provide evidence that risk-return models describe the neural processes underlying investment decisions well. Most importantly, the observed correlation between risk and brain activity in the anterior insula during choices supports risk-return models more than utility-based models because risk is an explicit component of risk-return models but not of the utility-based models.